Abstract
Modern procedures for solving geodetic boundary value problems are often based on the integral equation approach, employing representation formulae of different type for the mathematical description of the disturbing potential. Several alternative representations (single and double layer potentials as well as Brovar’s generalized single layer and volume potentials) and the resulting integral equations are considered for the simple Molodenskii problem. The integral equations and the corresponding solutions for the special case of a spherical boundary surface are derived and compared with respect to their properties. It is shown that the representations by Brovar’s generalized volume potential and by surface multipoles are not suitable due to numerical instabilities.
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Heck, B. (2003). Integral Equation Methods in Physical Geodesy. In: Grafarend, E.W., Krumm, F.W., Schwarze, V.S. (eds) Geodesy-The Challenge of the 3rd Millennium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05296-9_19
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DOI: https://doi.org/10.1007/978-3-662-05296-9_19
Publisher Name: Springer, Berlin, Heidelberg
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